Covering a certain social topic, people may form different opinions. Some opinions are irrational (e.g. rumors), while the other opinions are of rationality. The irrational opinions are spontaneously doubted because of the irrationality, while rational opinions are solid. The propagation of different opinions is affected by people's subjective communication tendency. On this basis, we propose an SIDR compartment model consisting of susceptible individuals, irrational individuals, doubters and rational individuals. Four meaningful equilibrium states and corresponding stability conditions are theoretically analyzed. By numerical simulation, we investigate the rationalization of public opinions. The results show that, the spontaneous loss of irrationality is conducive to the reduction of irrational individuals. However, when it is cooperated with the persuasion from rational individuals, the irrationality loss not always raises the number of rational individuals. Instead, susceptible individuals will occupy considerable population, hence the impediment to rationalization. In this sense, those irrational individuals sometimes also play a positive role in rationalization, because they lead the susceptible to form an opinion (irrational though), thus makes it possible for them to have doubt and further accept the rational opinion. (c) 2020 Elsevier B.V. All rights reserved.
